75q=-q^2+6250

Solution for 75q=-q^2+6250 equation:

75q=-q^2+6250

We move all terms to the left:

75q-(-q^2+6250)=0

We get rid of parentheses

q^2+75q-6250=0

a = 1; b = 75; c = -6250;
Δ = b2-4ac
Δ = 752-4·1·(-6250)
Δ = 30625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30625}=175$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-175}{2*1}=\frac{-250}{2}
=-125
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+175}{2*1}=\frac{100}{2}
=50
$